[EM] Show of hands voting. Non-Instant IRV, and Sequential Pairwise.

[Michael Ossipoff]

In show-of-hands voting, in a meeting, Approval has a problem--If the
A voters and B voters are a mutual majority, and, when votes are being
taken for B, the A voters approve B, then, when it's time to vote on
A, the B voters will know that they can win by not voting for A.

Score would help some--The A voters could give cautious strategic
fractional rating (SFR) to B. But, nevertheless, by the time it is
time to vote on A, it might be evident, from conditions, that the B
voters can win by not voting for A.

Non-Instant IRV:

In show-of-hands voting, IRV is sometimes done, without the "instant" feature:

Everyone votes for their favorite. The candidate getting fewest votes
is eliminated. Another vote is conducted, and, again, the candidate
getting fewest votes is eliminated. This s repeated till only one
candidate remains un-eliminated. This show-of-hands voting system has
been in use for a long time, and its users have seemed quite satisfied
with it.'

Sequential Pairwise (SP):

This is a familiar method, popular for meetings. I believe that it's
recommended in Robert's Rules, and used in many organizational and
legislative meetings.

The candidates are written in a vertical list on the blackboard. Their
order could be their order of proposal, or could be chosen by an
initial Plurality vote.

A 2-way vote is conducted between the top two. The winner goes against
the next candidate in the list, in a 2-way vote...and so on, till a
2-way vote has been done with the candidate at the bottom of the list.
The winner of that vote wins.

SP meets Smith, and therefore the Mutual Majority Criterion (MMC). It
doesn't have the chicken dilemma. As defined, the chicken dilemma is
when you don't know if Compromise's voters will defect, and you don't
know what to do. In SP, if Compromise's voters defect, and insincerely
vote over Favorite, someone that you and they like less than Favorite
and Compromise, you can observe that, and then not support Compromise
in hir subsequent pairwise votes.

Of course if Compromise and Worst come up for a pairwise vote first,
and you vote for Compromise over Worst, the Compromise voters won't
have an opportunity to defect againsts Favorite, because Favorite and
some other candidate (other than Compromise) won't be in a pairwise
vote until such time as Compromise is no longer in the running.

Of course SP has offensive strategy: If you think that X is more of a
threat to Favorite than Y is, then you could vote X over Y, even if
you like Y better than X.

But, as I said, that offensive strategy is observable, and the Y
voters can retaliate afterwards, by not supporting X, or by
insincerely voting others over X.

You might say that, given the fact that Com[romise voters have already
voted Worst over Favorite, and now it's your turn to vote between
Compromise and Worst, you might want to support Compromise, to keep
Worst from winning.

But it could be solemnly promised and agreed, in advance, that
defection would result in retaliation. When you vote Worst over
Compromise, in retaliation for Compromise voters' defection or
offensive strategy, you should realize that they, not you, made that
happen.  ...if it's undestood that the preferrers of Favorite and
Compromise all strongly prefer both to Worst, and detest Worst.

So I don't consider that offensive strategy to be a problem, and I
don't consider SP to have a chicken dilemma.

Sure, it isn't as deluxe as Schwartz Woodall, because of the
retaliation-need. But it's easier to count, when there are lots of
alternatives and no computer-counting program, and show-of-hands is
being used.

As I've said, the pairwise-count methods are computation-intensive,
and that is inherent in their goal and purpose.

Approval greatly reduces the count work, by just letting people vote
the pairwise preferences that are most important to them, as allowed
by Approval's simple rule.

SP, likewise, saves count labor by only looking at some pairwise preferences.

If there are N candidates, then SP votes between (N/2) times fewer
candidate-pairs than the pairwise-count methods, such as Schwartz
Woodall, Woodall, Condorcet-IRV/Benham, Beatpath,etc.

If there are lots of candidates, that could be important. If there are
only a few candidates, then just do Schwartz Woodall.

And yes, SP fails Pareto, but that isn't an important strategy
criterion. SP's longstanding popularity shows that Pareto failure
isn't important in a practical way.

Michael Ossipoff